It is very unusual to get any sort of pest in a spider plant. I have grown them for years and never had any sort of infestation. Since they are so easy to grow, I would just toss this plant. I suspect there is some sort of infestation in the soil. I also think that vinegar would hurt the plant, although they are as tough as nails. Vinegar is an acid and is corrosive. You could try some sort of insecticidal soap, but I don't think it is worth the effort. Toss it and start a new one in new soil.
I've been reading here that people are using vinegar to kill weeds and some have replied that it also kills thier grass so I would guess no. I would put the plant in the shower and wash it off. If you have a sprayer nozzle in the sink you could use that as well. You could also make up a soapy water solution and spray with that then rinse with clear water.
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